NEWTON'S EXPERIMENTS ON DIFFRACTION,' iO& 



where the integrals are to be taken between the limits w = y, w = S. The 

 brightness at the point x of the screen will then be proportional to the 



sum of the squares of the coefficients of sin---(yi—A — a — h) an(f 

 cos — (yt— A — a — b). 



A 



To consider in the second place a case in which the illumination is 

 produced in Fresnel's method. Let the distance from the origin of light 

 to the aperture be a', and from the aperture to the screen V. Let a 

 line be drawn from the origin of light perpendicular to the screen, and 

 let the limits of the aperture measured from this line, in the same 

 direction as the breadths of the parallelograms in Newton's case, be e and ^ 

 (the general letter for the distance of any point in this direction being p), 

 and let the limits in the direction perpendicular to this be rj + np, 6 + nj), 

 where m is constant. (It is readily seen that this implies the figure to 

 be rhomboidal, with two sides parallel to the length of the parallelograms 

 in Newton's case.) Let q be the general letter for distance in this second 

 direction : also let of and y' be the distances, in the directions of p and q, 

 of a point on the screen from the same line. The distance from the 

 origin of light to the point p, q, in the aperture is 



and the displacement there will therefore be proportional to 



The distance from the point p, q, in the aperture to the point or', y', on 

 the screen, is 



and this must be added to 



A + a' + ^ + ^,, 



in the expression for the displacement, in order to find the displacement 

 produced at the point x',y', of the screen by the wave diverging from 



